Sorry Richard, your post wasn't clear about what you wanted (I mistook the meaning of the words part of your request)
The Madden collection is at the Cambridge University Library, so (not surprisingly) won't be online at the Bodleian. Neither is it in the UCSB Broadside ballad collection. So you may be out of luck there.
Eliza's text is almost identical to the version printed by Roy Palmer - last line different, a few minor text changes and a slightly different chorus. The song appears to have been quoted in quite a few books (on a quick scan through Google). Masefield's Sailor's Garland has a 15 verse version as The Sailor Laddie..
Are you only interested in the versions of Roud 506 under the Rolling Sailor title (most are under different titles)?
And thanks Reinhard for confirming that the posted version here was as in Palmer. Palmer's notes say the first two verses are from James Gardner's, Above & Under Hatches (1906) p.16, (see it at archive.org as Recollections of James Anthony Gardner - though the actual page is a bit blurred in the online version), the remaining verses from the twenty-five of a garland text 'The Sailor Laddie, which the Roud index gives as Three Excellent New Songs (Chapbook) (Harding Garlands A1). The latter doesn't seem to be at the Bodleian. There are copies in VWML. Maybe Steve Gardham has a copy.